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The majority of models of inflation in string theory predict an absence ofmeasurable gravitational waves, r << 10^{-3}. The most promising proposals formaking string theoretic models that yield measurable tensor fluctuationsinvolve axion fields with slightly broken shift symmetry. We consider suchmodels in detail, with a particular focus on the N-flation scenario and onaxion valley/natural inflation models. We find that in Calabi-Yau threefoldcompactifications with logarithmic Kahler potentials K it appears to bedifficult to meet the conditions required for axion inflation in thesupergravity regime. However, in supergravities with an (approximately)quadratic shift-symmetric K, axion inflation may be viable. Such Kahlerpotentials do arise in some string models, in specific limits of the modulispace. We describe the most promising classes of models; more detailed studywill be required before one can conclude that working models exist.

Axion Inflation and Gravity Waves in String Theory